Paper 2026/2437

Confidential Error-Correcting Codes

Abstract

We introduce Confidential Error-correcting Codes (CECs), a new cryptographic primitive that enables reliable decoding from perturbed codewords while preserving message confidentiality. We formalize this primitive through three security properties: confidentiality, robustness, and soundness. To realize this goal, we develop a general framework for constructing CECs based on a Randomness-Security Separation (RSS) structure, which first encodes a nonce to introduce randomness and then masks the encoded payload with a pseudorandom function. Based on our RSS framework, we instantiate CECs, called Conc-CEC, using concatenated Reed-Muller and Reed-Solomon codes. The resulting Conc-CEC admits provable guarantees for all three properties. Notably, compared to PRCs (CRYPTO'24), another recent cryptographic primitive with error-correcting capability, CECs achieve significantly stronger concrete security guarantees under practical parameter settings. As a primary application of CECs, we further present CECMark, a watermarking scheme for AI-generated images. Our experiments on real-world generative image models show that CECMark consistently outperforms state-of-the-art watermarking methods, including Gaussian Shading (CVPR'24), PRCMark (ICLR'25), and T2SMark (NeurIPS'25). In particular, CECMark achieves higher robustness across all 56 evaluated perturbations and ensures a false positive rate below $10^{-5}$ without introducing side effects. Taken together, our work lays a novel cryptographic foundation for trustworthy watermarking schemes that, for the first time, unify provable security guarantees with strong practical reliability.